Optimal Reverse-Pricing Mechanisms

Reverse pricing is a market mechanism under which a consumer's bid for a product leads to a sale if the bid exceeds a hidden acceptance threshold the seller has set in advance. The seller faces two key decisions in designing such a mechanism. First, he must decide where in the process to collect the revenue—that is, whether to commit to a minimum markup above cost (and thus define the bid-acceptance threshold given cost) and whether to set a fee for the consumer's right to bid. Second, the seller must decide whether to facilitate or hinder consumer learning about the current bid-acceptance threshold. We analyze these decisions for a profit-maximizing small intermediary retailer selling to consumers who can also purchase the product in an outside posted-price market. The optimal revenue model is to charge a fee for the right to bid and then accept all bids above cost, rather than to set a positive minimum markup above cost. Avoiding minimum markups in favor of a bidding fee is more profitable because of increased efficiency arising from more entry by consumers and higher bids by the entrants. When consumers learn about the bid-acceptance threshold before they enter the market, efficiency increases further, and generating revenue through a bidding fee can compensate the seller for his loss of information rent when the competition from the outside posted-price firm is relatively weak.